Whole brain susceptibility mapping using compressed sensing

TLDR

Susceptibility derivation from image phase is hindered by ill‑conditioned filter inversion in certain k‑space regions, affecting the entire spectrum in regularized inversions but only the problematic areas in compressed‑sensing approaches. The study aims to use compressed sensing to compensate for k‑space regions where direct filter inversion is unstable. Compressed‑sensing compensation estimates only the ill‑conditioned k‑space regions, thereby avoiding instability across the full spectrum. The compressed‑sensing method produces susceptibility maps with markedly reduced streaking artifacts, outperforms regularization techniques, accurately depicts iron‑rich regions, provides clear white‑gray matter contrast, and shows strong linear correlations between iron content and susceptibility in deep nuclei. Published in Magn Reson Med, 2011; © 2011 Wiley‑Liss, Inc.

Abstract

Abstract The derivation of susceptibility from image phase is hampered by the ill‐conditioned filter inversion in certain k ‐space regions. In this article, compressed sensing is used to compensate for the k ‐space regions where direct filter inversion is unstable. A significantly lower level of streaking artifacts is produced in the resulting susceptibility maps for both simulated and in vivo data sets compared to outcomes obtained using the direct threshold method. It is also demonstrated that the compressed sensing based method outperforms regularization based methods. The key difference between the regularized inversions and compressed sensing compensated inversions is that, in the former case, the entire k ‐space spectrum estimation is affected by the ill‐conditioned filter inversion in certain k ‐space regions, whereas in the compressed sensing based method only the ill‐conditioned k ‐space regions are estimated. In the susceptibility map calculated from the phase measurement obtained using a 3T scanner, not only are the iron‐rich regions well depicted, but good contrast between white and gray matter interfaces that feature a low level of susceptibility variations are also obtained. The correlation between the iron content and the susceptibility levels in iron‐rich deep nucleus regions is studied, and strong linear relationships are observed which agree with previous findings. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.